Several types of media players exist in today's market place for reading and/or writing to various types of media discs. For example, reading and writing devices are known for reading from and writing to compact discs (CDs), digital video discs (DVDs), and other disc-based media formats. Each of these devices includes a laser lens for reading or writing electronic data on the media discs. Such laser lenses get dirty over time and require cleaning. Lens cleaning discs are insertable into the media player to clean the laser lens and may include one or more brushes that are configured to contact the laser lens as the disc rotates in the player. Cleaning disc brushes generally extend away from a surface of the disc that faces the laser lens and contact the laser lens when the disc is rotated by the device. The brushes thereby perform a wiping operation on the lens that cleans debris from the lens. In many instances, the brushes of the cleaning disc become pinched or jammed between the surface of the disc and the laser lens. This problem is notably prevalent in situations where the clearance between the disc and the laser lens is particularly small, such as in a high definition video disc player. Pinching and jamming of the brushes may scratch or otherwise damage the lens or the cleaning disc, or may prevent the disc from rotating, thereby reducing or altogether eliminating the ability of the cleaning disc to effectively clean the lens.